Mutual Invadability Implies Coexistence in Spatial Models

Richard Durrett

ISBN 10: 0821827685 / ISBN 13: 9780821827680

Verlag: Amer Mathematical Society, 2002

May have limited writing in cover pages. Pages are unmarked. ~ ThriftBooks: Read More, Spend Less 0.55. Bestandsnummer des Verkäufers G0821827685I4N00

Inhaltsangabe:

In (1994) Durrett and Levin proposed that the equilibrium behavior of stochastic spatial models could be determined from properties of the solution of the mean field ordinary differential equation (ODE) that is obtained by pretending that all sites are always independent. Here we prove a general result in support of that picture. We give a condition on an ordinary differential equation which implies that densities stay bounded away from 0 in the associated reaction-diffusion equation, and that coexistence occurs in the stochastic spatial model with fast stirring. Then using biologists' notion of invadability as a guide, we show how this condition can be checked in a wide variety of examples that involve two or three species: epidemics, diploid genetics models, predator-prey systems, and various competition models.

Bibliografische Details

Titel: Mutual Invadability Implies Coexistence in ...
Verlag: Amer Mathematical Society
Erscheinungsdatum: 2002
Einband: Unknown
Zustand: Very Good
Zustand des Schutzumschlags: No Jacket